Why are most COVID-19 infection curves linear?

TL;DR

This paper explains the observed linear growth of COVID-19 cases in some countries during the containment phase by analyzing contact network structures, showing that below a critical contact number, linear growth is inevitable, challenging traditional models.

Contribution

The authors introduce a contact network-based model that accounts for linear infection growth, providing a new explanation for COVID-19 dynamics during containment phases.

Findings

Linear growth occurs when social contacts are below a critical threshold.

The model accurately reproduces infection curves for US and Austria.

Standard compartmental models rarely predict linear growth, unlike the network-based approach.

Abstract

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of non-pharmaceutical interventions that pushed the growth rate below the recovery rate. In this new phase of the pandemic many countries show an almost linear growth of confirmed cases for extended time-periods. This new containment regime is hard to explain by traditional models where infection numbers either grow explosively until herd immunity is reached, or the epidemic is completely suppressed (zero new cases). Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts, $D_c$, below which linear growth and low infection prevalence must occur. Above $D_c$ traditional epidemiological dynamics takes place, as e.g. in SIR-type models. When calibrating our corresponding model to empirical estimates of the transmission rate and the number of days being contagious, we find $D_c\sim 7.2$. Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household-size (about 2.5), we reproduce actual infection curves with a remarkable precision, without fitting or fine-tuning of parameters. In particular we compare the US and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero.